In order to optimize network performance and improve network utilization, it is desirable to understand characteristics of traffic transmitted through a data network. A number of mathematical models are used to model the statistical properties of real world network traffic. Through the models, a set of traffic patterns may be generated to mimic the real world network traffic, and the set of traffic patterns can be used to analyze and optimize network performance such as providing ways to handle congestion and estimate capacity.
One basic model for a traffic source is the Bernoulli source model. The Bernoulli source model describes a non-correlated packet source, i.e., new packets are generated based on probabilities that are independent of any previous event. The load offered by a Bernoulli traffic source can be specified by p, a probability of a packet arrival in a given time interval, which is independent of arrivals in previous time intervals. Thus, the probability of arrival can be denoted as Prob (1 arrival)=p, and the probability of no arrival can be denoted as Prob (0 arrival)=1−p. The Bernoulli source model is a memoryless process. That is, knowledge of a past arrival does not help predict a current or future arrival.
Another model for traffic source is an On-Off source model. In the On-Off source model, an On-Off source operates as a two state Markov modulated process (MMP). In the ON state, the source generates a packet with a probability. In the OFF state, no packets are generated. Two parameters are needed for the On-Off traffic source: an offered load and an average burst length. An MMP changes the injection process for bursty traffic. In an MMP, the rate of a Bernoulli injection process is modulated by a current state of a Markov chain.
FIG. 1 illustrates a two state Markov traffic source model. A traffic source may be modeled using the ON and OFF states. In the ON state, the traffic source has an injection rate of r1; in the OFF state, the traffic source has an injection rate of 0. The probability of transition from the OFF state to the ON state is a, and the probability of transition from the ON state to the OFF state is b. The two state Markov traffic source model represents a bursty injection process, where during bursts, injections occur with an overall rate of r1 and random inter-packet delays; and outside the bursts, no injection is allowed. The average burst length is 1/b and the average time between two bursts is 1/a. The larger the ratio of b to a, the more intense is the traffic arrival during a burst period.
The two state Markov traffic model is a special case of Markov-based traffic models. In general, a Markov-based traffic model is represented as an n-state continuous time Markov process (the more the number of states, the more the variety of traffic patterns, rates, etc.). The n-state continuous time Markov process may be presented asM={M(t)}, t=0 to ∞,where the state space is {S1, S2, . . . , Sn}. Thus,M(t){S1,S2, . . . ,Sn}.
The Markov process M stays in state Si for an exponentially distributed holding time and then jumps to state Sj with probability Pij. More generally, all the state transitions are governed by a probability state matrix P=[Pij], where Pij represents the probability of transition from state i to state j. Using the Markov process, the probability of traffic arrival is determined by a specific state in which the Markov process M is in. For example, assume that while M is in state Sk, the probability of traffic arrivals is completely determined by k, and this holds true for every 1≦k≦n. When M undergoes a transition to, for example, state Sj, then a new probability takes effect for the duration of state Sj. The most commonly used Markov modulated process model is the Markov Modulated Poisson process (MMPP). In that case, the modulation mechanism simply stipulates that in the state Sk of M, traffic arrivals occur according to a Poisson process at rate λk. As the state changes, so does the rate. These traffic source models above have been applied to traditional network equipment such as special purpose network devices (e.g., routers and switches). Yet, a new networking architecture, software-defined networking (SDN), is gaining popularity among carriers and enterprises, and SDN has specific features worth considering in applying traffic modeling.
The software-defined networking (SDN) is a network architecture that aims at decoupling control plane functions from data plane functions such that separate apparatuses may be utilized for different functions. In the SDN architecture, network intelligence and states are logically centralized, and the underlying network infrastructure is abstracted from the applications. As a result, networking may be simplified and new applications become feasible. For example, network virtualization can be accomplished by implementing it in a software application where the control plane is separated from the data plane. Also, a network administrator of a SDN system may have programmable central control of network traffic without requiring physical access to the system's hardware devices.